Large Language Models for Mathematical Analysis
This work addresses a critical gap in mathematical reasoning for AI researchers, though it is incremental as it builds on existing LLM fine-tuning methods applied to a new domain-specific dataset.
The authors tackled the gap in mathematical analysis problem-solving by creating the DEMI-MathAnalysis dataset and a guiding framework, which improved LLMs' proof generation capabilities with significant enhancements in logical, complete, and elegant proofs.
Mathematical problem-solving is a key field in artificial intelligence (AI) and a critical benchmark for evaluating the capabilities of large language models (LLMs). While extensive research has focused on mathematical problem-solving, most existing work and datasets concentrate on computational tasks, leaving gaps in areas like mathematical analysis, which demands rigorous proofs and formal reasoning. We developed the DEMI-MathAnalysis dataset, comprising proof-based problems from mathematical analysis topics such as Sequences and Limits, Infinite Series, and Convex Functions. We also designed a guiding framework to rigorously enhance LLMs' ability to solve these problems. Through fine-tuning LLMs on this dataset and employing our framework, we observed significant improvements in their capability to generate logical, complete, and elegant proofs. This work addresses critical gaps in mathematical reasoning and contributes to advancing trustworthy AI capable of handling formalized mathematical language. The code is publicly accessible at LLMs for Mathematical Analysis.